As a project manager, how to deal with a member who thinks I must be more expert than every member of a team to be able to lead them. And refuses my management?

A leader or manager need not to be expert in all functional matters. Leadership is about assimilating, learning and understanding your role as guide and to provide stewardship in an organization.  So, you need to be confident about yourself first.

Now, please discuss with the member privately what the issue is? There may be some other issues with the member- try to explore the issue and solve. Explain to the member about the corporate goal and effort of everybody is necessary to achieve that goal. Also, try to provide growth opportunity for that specific member. Hope the issues will be solved

I would suggest this team member need to be educate and let him fully understand the leadership or management concept.  Leadership is more focused on collaborative efforts and collaborative decision making  not single man decision this concept need to understand by whole team then only high performance team can be formed.  Any misalignment among the team will impact negatively on the goals and targets.  So communicate with this staff as soon as possible and let him know this and  listen to him what he want to say/suggest, sure it will conclude to build more healthy relationship between manager and team.

One from about team members dosen't effect in the process of managing a project , generally try to give him another chance and with the time he will discover that he was in the wrong side.You have been demanded to prove your effeciancy in leadership and management for your staff and don't care by isolated individual opinion .

If this issue arise, definitely there is something wrong and needs to be fixed, maybe with your team member, he may lack of capability and needs a technical support to do assigned tasks.

Or it maybe you or the way you manage your team, you may not a good listener or try to impose yourself in technical issues. Generally you need to remodel your team and here is somethings to think about.

- define an exact roles and responsibilities for each team member, you must chose the right one for the right task (ask someone from HR to help you with this)

- create proper communication channels with interdependence and internal intersections.

- never micromanage tasks and deal with it as black boxes, focus on providing managerial support and let team focus on technical, let them know that you do the demotivational tasks.

- defined common goals and objectives with awareness of commitment and individual accountability.

- you may need to assign technical lead, find the most experience team member and make him the technical lead who will be responsible about technical issues. ( this action is the most important one to stop conflict immediately) 

• Sit down with him
• List down all the functional areas that you cover
• Ask him what number/percentage of people with specialization in all the areas might be available and what is the requirement.
• He must understand that one person can not master all the areas to lead a multi-functional team. And it is the choice of the project directors or whosoever is incharge to choose the person to lead. And everyone else must cooperate with the selected leader.
• If he doesn't understand, he shall be replaced.

listen and speak to all team and try to deliver message to them and understood what they need